"Get
your facts first, and then you can distort them
as much as you
please."

Mark
Twain (as quoted by Kipling)

FOR THOSE NEW to the news, in the past few
years, emerald traders have become the pariahs of our business,
ranking right down there with terrorists, child pornographers and
those who propose an increase in the minimum wage. If one reads
the reports correctly, they tend to lurk in trench coats outside
of playgrounds, ever ready to corrupt the morals of the nation's
youth. Their weapon of choice: Opticon. By slipping a treated emerald
from beneath their cloaks, they induce in their victims a permanent
state of moral turpitude, leading them across to the dark side,
a state of total and utter depravity.

Extreme
rhetoric? Perhaps, but the mere mention of Opticon
today seems to induce a type of collective hysteria
that borders on paranoid schizophrenia. Just why
is a mystery to this writer.

Figure 1 Due
to the conditions under which they form, most emeralds
contain numerous fractures and openings. This photo shows
the classic three-phase inclusion of a Colombian emerald,
consisting of a negative crystal filled with a gas bubble,
a halite crystal and a brine solution. If cutting exposes
this inclusion to the surface, it will fill with air, producing
reflection. Such inclusions are typically filled with oil
or resin to reduce the amount of reflection. (Photo: R.W.
Hughes)

Let's
get some facts. The stressful geologic conditions under which
emerald forms means that virtually all natural emeralds contain numerous
surface-reaching fractures and openings. Dealers reduce the visibility
of these by filling them with a fluid. Traditionally, such fillers
have been oils of various types, cedarwood oil being a common
one;
today, resins are also used. This type of enhancement process
is one of the oldest in the business, with reports on it dating back
over 600 years.

Figure 2 Another
negative crystal in a Colombian emerald, this one containing
more than one daughter crystal.
(Photo: R.W. Hughes)

Just
what is Opticon? It is a type of epoxy resin, and has been sold
for decades. Indeed, it has been advertised as a fracture sealant
in the Lapidary Journal since at least the early 1960s.
What are some of the claims that have been made about Opticon?
Some believe that, since Opticon is a type of epoxy, it is equivalent
to gluing a stone together. The reality is far more mundane.
Epoxy resins such as Opticon come in two parts – a resin
and a hardener. Typically, for emerald treatment only the resin
is used. The hardener, if used at all, is used solely to seal
the surfaces. Thus Opticon is not used to "glue stones together."

But
by far the strongest argument made by gemologists
against Opticon is that it (and related resins) are
so good at cloaking fractures that they disappear
completely. The following is from the trial transcripts
of the infamous Fred Ward emerald case:

In the case of oil, it's very efficient. It's been a traditional process.
In the case of Opticon, it's about 30 to 40 percent
more efficient than the oil. In other words, it mask
[sic] the fractures
much more completely than oil ever could.

Masking
refers to the ability of a filler to make a fracture invisible,
and is a function of how closely the refractive index (RI)
of the filler matches that of the gem being enhanced. The closer
the RI's
of the two substances, the better the masking. If the RI's
are identical, no reflection will take place when light strikes
the filled fracture, making it completely invisible.

In
an effort to separate fact from fancy, the author did a mathematical
modeling of Opticon versus the traditional cedarwood oil (see the
above illustration). Incredibly, this shows that, contrary to the
above testimony, differences between the reflectivity of Opticon
versus cedarwood oil are minor, on the order of 6–7%, far
less than the 30–40% claimed. Suddenly, facts in hand, Opticon
doesn't look so bad after all.

Emerald
is among the most beautiful precious stones this
planet has ever produced. It also tends to contain
large numbers of surface-reaching fractures and openings.
Thus the prevalence of clarity enhancements.

Figure
4 Filling
fractures with a resin of similar RI to the host
emerald typically produces a color flash effect.
In this case, an orange flash is seen. (Photo: R.W.
Hughes)

Figure
5 The
same stone as above, but tilted slightly, so that
the color flash is now blue. (Photo: R.W. Hughes)

The
Luddites who pine for an enhancement-free world are merely guilty
of flights of fancy. For that, they can be forgiven. Oh, my dearies,
those days are gone. Long gone. You must let them go…

Unfortunately,
it is far harder to forgive the self-appointed consumer
advocates whose anti-Opticon vitriol and diatribes
represent a de-facto crusade for the continuation
of unstable enhancements like cedarwood oil. Today,
those actions threaten to put a dagger through the
very heart of the emerald business, an honorable
trade which revolves around one of nature's
most majestic creations. I simply cannot go along
with it.

Author's Afterword

Note

Since publication,
I have, with the most generous help of John Emmett and Karen Palmer
of Crystal Chemistry (22721 NE 123rd Circle, Brush Prairie, WA
98606) refined the math to produce a more exact analysis of reflectivity
from an oil-filled interface in emerald. The following table gives
exact numbers. The emerald is assumed to have an RI of 1.58.

What this table clearly demonstrates is that
filling a fissure or crack in an emerald with any of the
commonly used fillers removes the lion's share of reflection
when compared with air. Comparing the various fillers to one another
reveals
only slight differences in reflectivity.

Filler RI

Critical
Angle

Reflectance Percentages
at Various Angles of Incidence

0°

10°

20°

30°

40°

50°

60°

70°

80°

90°

Air n = 1.000

39.27°

5.05

5.07

7.42

100

100

100

100

100

100

100

n = 1.500

71.69°

0.07

0.07

0.07

0.08

0.11

0.25

1.05

17.01

100

100

n = 1.517

73.77°

0.04

0.04

0.04

0.05

0.07

0.14

0.58

6.28

100

100

n = 1.531

75.69°

0.02

0.02

0.03

0.03

0.04

0.08

0.32

2.82

100

100

n = 1.550

78.82°

0.01

0.01

0.01

0.01

0.01

0.03

0.11

0.77

100

100

n = 1.570

83.55°

0.00

0.00

0.00

0.00

0.00

0.00

0.01

0.07

1.73

100

The following is John Emmett's
explanation of the optics behind the above calculations. They
make reference to an Excel spreadsheet which John and Karen
created. Should you be interested in playing with this file, download it here. But be forewarned, neither
John Emmett nor myself will be providing technical support
for the use of this file. The Emmett tech-support hotline is
already worn out on this problem and I, myself am mathematically
challenged.

All cracked up (with
no place to go)

To: Dick Hughes
From: John L. Emmett

Subject: Your Problem (but not your only
one)

In this spreadsheet there are only
four numbers you can enter: n1 in two places,
and n2 in two places. The spreadsheet calculates
the Relative Index of Refraction n = n2/n1,
and the Critical Angle so don't try to enter these.
From these numbers the spreadsheet calculates all of the
reflectivities. Note you can change Emerald to any gemstone
name you want, and likewise you can change the crack content
to anything you want. Note that when you change the index
of refraction of anything, the spreadsheet recalculates everything.
In addition the reflectivity calculations are duplicated
so you can directly compare an empty crack with a filled
crack by seeing the numbers next to each other.

Now
for some explanations. The geometry, nomenclature,
and equations used are presented in Grant
R. Fowles' Introduction to Modern
Optics (1968, Holt, Rinehart and Winston,
New York). The geometry is shown in Figure
2.9, page 48 of this reference. The incident
light ray is always in the region with the
index of refraction n1, regardless
of the relative index of refraction of the
two materials. The reflected ray is always
in region n1 also. The transmitted
ray is always in the region with index n2.
With these conventions, the spreadsheet always
calculates the reflectivities correctly whether
the incident ray is in the lower or higher
refractive index region. Thus this spreadsheet
is quite general, but you have to think carefully
about what you are doing.

The
equations programmed into the spreadsheet
are 2.58 and 2.59 on page 51 of the reference.

Where E'/E is the amplitude reflectivity
of the electric field of the light, and R is the light intensity
reflectivity.

The
Critical Angle is that angle where the reflectivity
becomes 100%, and remains 100% for all larger
angles. This occurs only for the situation
where n<1.0. The equation for the critical
angle is just:

Now
what do TE and TM mean? As you know, there are two polarization
directions of light which are perpendicular to each other
and perpendicular to the direction of propagation of the
light ray or beam. Unpolarized light can be described as
equal amounts of the two polarizations. Because the reflectivities
of interfaces are dependent on the polarization of the incident
ray, we have to calculate it for each polarization. That
is why the spreadsheet has two columns for the reflectivity.
There are many ways to denote the two polarizations. This
book has chosen TE (transverse electric) and TM (transverse
magnetic). What does that mean? First, remember that the
polarization direction and the electric field vector direction
of light are the same thing. Second, transverse in this context
means "perpendicular." Perpendicular to what? Perpendicular
to the plane of incidence. This is an imaginary plane that
contains both the incident and reflected ray. In my drawing
Figure 1a, the plane of incidence is the sheet of paper.
(Note: all my drawings are for the situation where n1>n2 which
is why the transmitted ray bends the other way from the drawings
in the book.) Note that in Figure 1a the little circles on
the light rays are meant to denote the ends of the polarization
direction arrows shown more clearly for the other polarization
in Figure 1b. Now what does TM mean? Remember that light
is made up of both an electric field and a magnetic field
and that their vectors are mutually perpendicular to each
other. So TM just means that the magnetic field vector is
perpendicular to the Plane of Incidence. Since we normally
think of polarization in terms of the electric vector direction,
I have shown that as the arrows in the TM case in Figure
1b. Since light in most observational situations is made
up of both polarizations we average the two single polarization
reflectivities to calculate the real single surface reflectivity.

Now
on to the explanation of the problem I have
calculated for you. As I understand your
current interest, it is to calculate the
reflectivity of a crack in a gemstone filled
with anything like air, oil, Opticon, kangaroo
piss, or whatever. Thus I have set up the
problem in that way, i.e., the incident ray
is in the gemstone (index n1)
and is incident on the crack (index n2).
This is shown in Figure 2. Now comes the
subtle part. Note that there are really TWO
reflections that count towards what you see;
the reflection off the top of the crack AND
the reflection off the bottom of the crack.
Thus the reflectivity from the first two
reflections of the crack is R + R(1–R)2,
where R is the single surface reflectivity.
For low reflectivities, this nearly DOUBLES
the single surface reflectivity calculated
in the spreadsheet! Don't forget this.
Actually there are many more reflections
but they contribute very little additional
intensity (see figure 2).

The
enclosed spreadsheet has a lot of #NUM! entries
courtesy of Excel. What is that all about?
If you look at Equation 2.58 or 2.59 for
the case where n<1.0, you can see that
for some angles it is possible for the quantity
under the square root sign to be negative.
As you know, you can't take the square
root of a negative number. Well actually
you can, and the result is called a complex
number because it contains two parts, a real
part and an imaginary part denoted by the
multiplier "i" which is equal to
square root(-1). (I know you don't want
to hear about this [your're
right, I don't] but I must persist
a little longer.) When you square a complex
number to get to get the intensity reflectivity,
you multiply the complex number (like a +
ib) by its complex conjugate (which is a – ib).
The result for the equations we are using
is 1.0, that is the reflectivity is 100%
for any complex number reflectivity. Now
this simple Excel spreadsheet does not know
about complex numbers, so when faced with
taking the square root of a negative number
it shouts HELP! (#NUM! in Excelspeak). So
you know what to do, OK? Whenever you see
#NUM! In the reflectivity column, just read
it as 100%. Now notice another thing. The
reflectivity changes relatively slowly with
increasing angle until you near the critical
angle where it increases very rapidly. Thus
you go from a few tens of percent reflectivity
to 100% in less than one degree! Positively
magical!

Now
examine the reflectivity columns in the spreadsheet
for the case where the indices of refraction
of crack filler and emerald differ by only
0.02. Note that the normal incidence reflectivity
is only .004%! If it is really this low,
why can you see the crack at all? Its simple;
either the surface is not emerald or it is
not planar. Most cracks contain mineral alteration
products or other impurities which have been
deposited in the crack. Even boiling in acid
does not fully remove these materials. These
materials have a color contrast to the emerald
which makes them more visible, or have indices
of refraction which are different than emerald
causing additional reflection. However, it
is important to remember that even if it
was totally an emerald surface, but that
surface had a fine roughness, the oil, with
its finite viscosity, might not completely
wet the surface and thus not completely reduce
the reflectivity.

Another
point I might make is that the closeness
of the index match is not too important.
Just use the spreadsheet to do an example
or two for yourself. Thus the practice of
filling tourmaline fractures with spermaceti
(n=1.43) works quite well as most tourmaline
fractures are very clean.

I
hope the foregoing answers your questions
adequately.

Sincerely,
John Emmett

For more on the fracture filling of emerald,
see this excellent article:

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